package DoExercise.HSP_ZCY.A008_树.A001_普通二叉树.二叉树递归套路_找可能性;


/**
 *
 *
 * 满二叉树的性质
 * 高度为K的树中的节点有 Math.pow(2,k)-1
 *
 */
public class Code02_是否是满二叉树
{
	
	public static void main(String[] args)
	{
		int maxLevel = 5;
		int maxValue = 100;
		int testTimes = 1000000;
		for (int i = 0; i < testTimes; i++)
		{
			Node head = generateRandomBST(maxLevel, maxValue);
			if (isFull1(head) != isFull2(head))
			{
				System.out.println("Oops!");
			}
		}
		System.out.println("finish!");
	}

	
	public static class Node
    {
        public int value;
        public Node left;
        public Node right;
        
        public Node(int data)
        {
            this.value = data;
        }
    }
    
    public static boolean isFull1(Node head)
    {
        if (head == null)
        {
            return true;
        }
        int height = h(head);
        int nodes = n(head);
        return (1 << height) - 1 == nodes;
    }
    
    public static int h(Node head)
    {
        if (head == null)
        {
            return 0;
        }
        return Math.max(h(head.left), h(head.right)) + 1;
    }
    
    public static int n(Node head)
    {
        if (head == null)
        {
            return 0;
        }
        return n(head.left) + n(head.right) + 1;
    }
    
    public static boolean isFull2(Node head)
    {
        if (head == null)
        {
            return true;
        }
        Info all = process(head);
        return (1 << all.height) - 1 == all.nodes;//深度为k的二叉树至多有2{k}-1个结点
    }
    
    public static class Info
    {
        public int height;//高度
        public int nodes;//节点数量
        
        public Info(int h, int n)
        {
            height = h;
            nodes = n;
        }
    }
    
    public static Info process(Node head)
    {
        if (head == null)
        {
            return new Info(0, 0);
        }
        Info leftInfo = process(head.left);
        Info rightInfo = process(head.right);
        int height = Math.max(leftInfo.height, rightInfo.height) + 1;
        int nodes = leftInfo.nodes + rightInfo.nodes + 1;
        return new Info(height, nodes);
    }
    
    // for test
    public static Node generateRandomBST(int maxLevel, int maxValue)
    {
        return generate(1, maxLevel, maxValue);
    }
    
    // for test
    public static Node generate(int level, int maxLevel, int maxValue)
    {
        if (level > maxLevel || Math.random() < 0.5)
        {
            return null;
        }
        Node head = new Node((int) (Math.random() * maxValue));
        head.left = generate(level + 1, maxLevel, maxValue);
        head.right = generate(level + 1, maxLevel, maxValue);
        return head;
    }
    
   
}
